DESCRIPTION (adapted from the Abstract): The dynamic nature of interactions between the human immunodeficiency virus (HIV) and the human immune system is complex and remains poorly understood in spite of recent important findings about the kinetics of viral and T-cell replication and clearance and the identification of cell-surface-corecptors for HIV entry. Developing accurate descriptions and a deeper understanding of the interactions between HIV and the immune system during the acute and early stages of HIV infection is critical to the evaluation of new, promising therapeutic regimens. Mathematical models, in the form of system of deterministic or stochastic rate equations, provide the most natural and convenient framework for formal descriptions of interactions between HIV and various compartments of the human immune system. Various simplified biological models for these interactions have been translated into such mathematical models and published by numerous research groups. Most of these models are focused on descriptions of the long-term course rather than the acute/early stage of HIV infection. No serious and systematic study has been made of the mathematical and probabilistic properties of these models. Typically, these models have been fit to data from few, select patients using statistical models, and methods that give virtually no serious attention to assessing sources of variability across patients. Finally, no careful and comprehensive comparative study has been made of these models with respect to their ability to describe accurately systematic patterns in longitudinally-collected virolgical and immunological data and to predict clinical outcomes. This Principal Investigator proposes to perform a systematic assessment of mathematical models for interactions between HIV and the human immune system with a particular emphasis on the utility of these models for describing acute and early stage of HIV infection. He and his colleagues will refine the formulation of these mathematical models and derive from them statistical models in which important sources of variation in observable analogs of model variables are acknowledged. They will develop and implement formal statistical methods to fit these models to data from clinical studies of acute/early HIV infection and perfrom a data-based comparative study of models. Through existing and ongoing collaborations with clinical researchers, they will use the models and methods to address specific scientific questions that are posed in the context of clinical studies.